Question: $f(x)=\dfrac{1}{8x+3}$ $g(x)=12-5x$ Write $f(g(x))$ as an expression in terms of $x$. $f(g(x))=$
Solution: Let's write $g(x)$ as the input to function $f$. $f({g(x)})=\dfrac{1}{8({g(x)})+3}$ Since $g(x)=12-5x$, this becomes: f ( g ( x ) ) = 1 8 ( 12 − 5 x ) + 3 = 1 96 − 40 x + 3 = 1 99 − 40 x \begin{aligned} f({g(x)})&=\dfrac{1}{8({12-5x})+3}\\ \\ &=\dfrac{1}{96-40x+3}\\ \\ &=\dfrac{1}{99-40x}\ \\ \end{aligned} Note: We simplified the result to obtain a nicer expression, but this is not necessary. The answer: $f(g(x))=\dfrac{1}{99-40x}$